102avellan Cavitation

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Scientific Bulletin of the

Politehnica University of Timisoara

Transactions on Mechanics Special issue

The 6thInternational Conference on

Hydraulic Machinery and Hydrodynamics

Timisoara, Romania, October 21 - 22, 2004

INTRODUCTION TO CAVITATION IN HYDRAULIC MACHINERY

Franois AVELLAN, Professor

Laboratory for Hydraulic Machines, School of Engineering

EPFL Swiss Federal Institute of Technology Lausanne

Avenue de Cour 33 Bis, CH-1007, Lausanne, Switzerland

Tel.: +41 21 693 2524, Fax: +41 21 693 3554, Email: [email protected]

ABSTRACT

Design, operation and refurbishment of hydraulic

turbines, pumps or pump-turbine are strongly related

to cavitation flow phenomena, which may occur in

either the rotating runner-impeller or the stationary

parts of the machine. The paper presents the cavitation

phenomena featured by fluid machinery including

type of cavity development related to the specific

speed of machines in both pump and turbine mode,

the influence of the operating conditions, such as load,

head and submergence. Therefore, for each type of

cavitation illustrated by flow visualization made at

the EPFL testing facilities, the influence of cavitationdevelopment on machine efficiency, operation and

integrity are discussed.

KEYWORDS

Cavitation, Hydraulic Machinery and Systems, Model

Testing

NOMENCLATURE

A [m2

] Area of the Flow Cross Section

QC

A

= [ms-1] Mean Flow Velocity

Cm [ms-1

] Meridian Velocity Component

Cu [ms-1

] Circumferential Velocity Comp.

cp p

CpE

= [-] Static Pressure Factor

D [m] Runner Reference Diameter

1 2E gH gH=

[Jkg-1

] Specific Hydraulic Energy

EFr

gD= [-] Froude Number

NPSE [Jkg-1

] Net Positive Suction Energy

P [W] Mechanical Power of the Machine

hP QE= [W] Machine Hydraulic PowerQ [m

3s

-1] Discharge

2

DR= [m] Runner Reference Radius

U R= [ms-1] Circumferential Velocity

W C U= uur ur ur

[ms-1

] Relative Flow Velocity

Z [m] Elevation

aZ [m] Elevation of the Tail Water Level

refZ [m] Machine Reference Elevation

rde [-] Factor of Specific Energy Losses

for the Machine Draft Tubek [-] Geometric Factor

g [ms-2

] Acceleration Due to Gravity2

2

p CgH gZ

= + +

[Jkg-1] Mean Specific Energy

s r ah Z Z= [m] Machine Setting Level

n [s-1

] Speed of Revolution

p [Pa] Absolute Static Pressure

ap [Pa] Atmospheric Pressure

vp [Pa] Vapor Pressure

rgH [Jkg

-1] Specific Energy Loss

v

E

p p

E

= [-] Local Cavitation Factor

2

c

= [-] Cavitation Number

2 2

2E

R

= [-] Specific Hydraulic Energy Coeff.

2 2

2c

NPSE

R

= [-] Net Positive Suction Specific

Hydraulic Energy Coeff.

2 2

2 rr

gH

R

= [-] Energy Loss Coefficient


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[-] Efficiency

3

Q

R

= [-] Flow Coefficient

0 [-] Whirl Free Flow Coefficient

[kgm-3

] Water Density.

[-] Thoma Number

i [-] Value of corresponding to the

onset of cavities

0 [-] Lowest value of for which the

efficiency remains unchanged as

compared to cavitation free op.

1 [-] Lowest value of as compared to

cavitation free operation for

which an efficiency drop of 1%

is noticed

[rads-1

] Runner Angular Velocity

Subscripts and Superscripts1 High Pressure Side of the Machine

2 Low Pressure Side of the Machine

c Low Pressure Side of the Runner

1. INTRODUCTION

Design, operation and refurbishment of hydraulic

turbines, pumps or pump-turbine are strongly related

to cavitation flow phenomena, which may occur in

either the rotating runner-impeller or the stationary

parts of the machine. The economic trend to increase

the specific power of the machine combined with the

modern operating conditions to operate the machine

over an extended range of discharge and specific

energy challenges the scientific community to develop

advanced knowledge of cavitation physics for this

type of machines. The paper presents the cavitation

phenomena featured by fluid machinery including

type of cavity development related to the specific

speed of machines in both pump and turbine mode,

the influence of the operating conditions, such as load,

head and submergence. Therefore, for each type of

cavitation illustrated by flow visualization made atthe EPFL testing facilities, the influence of cavitation

development on machine efficiency, operation stability

and integrity are discussed.

After introducing the general definitions and notations

in use in the field of hydraulic machinery, we describe

how the level setting of a hydraulic machine through

so called cavitation tests of reduced scale models.

Then we present for each type of machines, storage

pumps or pump turbines, Francis turbines and Kaplan

or Bulb turbine the different types of cavitation de-

velopments and the resulting performance alteration

and risk of erosions.

2. MODEL TESTING

2.1. General defini tion and notation

We examine in this paper the case of reaction hydraulicmachines including hydro-turbine, storage pump or

pump-turbine. Irrespective of the flow direction, thesubscript 1 defines the high pressure reference section

of the machine and the subscript 2 the low pressurereference section, as defined Fig. 1. The low-pressuresection of the runner is quoted with the subscript c .

Fig. 1 General sketch of a run-off power plant withKaplan Turbines.

By introducing p, the absolute pressure, Z, theelevation of a point and Cthe mean velocity defined

by the ratio between the discharge Qand the sectionareaA, gH, the mean specific hydraulic energy of agiven flow passage cross section, is defined as:

2

2

p CgH gZ

= + + [Jkg-1]

where is the water density and g the gravityacceleration.

Therefore, the specific hydraulic energy E of themachine is defined as the difference of the meanspecific energy values between the high and the low-

pressure limiting sections of the machine.

1 2E gH gH=

The breakdown of the expression of the mean specifichydraulic energy gives the following expression forE:

2 2

1 1 2 22

1

2 2

p C p CE gZ gZ

= + + + +

[Jkg-1

]

The product of the discharge by the machine specific

energy then defines the hydraulic powerh

P of the

machine

hP QE= [W]

The mechanical power P of the machine includingthe mechanical power dissipated in guide bearings,thrust bearings and shaft seals of the hydraulic machine,is related to the hydraulic power by the overall effi-

ciency, , of the machine by the following definitions:

hPP

= for a pump andh

PP

= for a turbine.


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Geometrical and kinematical similarity principles

allow defining the dimensionless terms, which

determine the hydraulic characteristics of the

machine.

The angular velocity and the reference radius R

of the machine runner/impeller define the reference

area2

R and the reference specific kinetic energy1

2

2 2R , which in turns provide the definition of

and , the dimensionless discharge and energy

coefficients.

3

Q

R

=

2 2

2E

R

=

All along this paper, we will use preferably these

coefficients since they are conveniently directly

proportional to the discharge Q and the specific

energyE.

Therefore, for any machine at a given setting, theopening angle of the guide vanes the discharge-energy

relations will collapse to a single function whatever

the runner/impeller rotational speed. For every opening

angle , we can plot the - characteristic as per

Fig. 2;

( ), =

Thus, the set of discharge and specific energy coeffi-

cients, , , and, , the opening angle of the guide

vanes, defines the operating conditions, for which

we can express the efficiency :( ), , =

In a similar way, we can plot on the diagram, - ,

the contours of efficiency iso-values to define the so-

called efficiency hill chart of the machine, see Fig. 2.

85%

90,5 %

91,5 %

80%

20.0 25

.0

85%

91 %80%7

0%

0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0,30 0,32 0,34

0.5

0.7

0.9

1.1

1.3

(-)

(-)

90 %

Fig. 2 Typical hill chart of a Francis turbine, 0.500= .

For real flow, viscous and turbulence dissipation

influences the machine efficiency and leads to the

so-called scale effect between reduced scale model

and full-scale prototype.

2.2. General Model tests

According to IEC 60193 standard, [1], model testsrequire that the geometric, the kinematics and thedynamic similitude principles be fulfilled between

model and prototype. Model dimensions must besufficient to achieve an excellent geometrical simi-

larity with the prototype; the typical outlet diameterD of Francis and Kaplan runners is of the order of0.3 - 0.4 m. Test installations should fulfill require-ments of the IEC standards regarding their capacity.

As an example, a view of the PF1 EPFL universal testrig for all types of reaction machines, turbines, pumpsand pump-turbines is reported Fig. 3. This test righas a 900 kW maximum pumping power, leading totest heads of up to 100 m (1'000 Jkg

-1) and a maxi-

mum flow rate of 1.4 m3/s. The dynamometer is limited

to a 320 kW maximum generated power at 2'500 rpm.

In general, a test procedure consists in measuring:

the overall hydraulic characteristic of the machineand the corresponding efficiency hill chart over awide range of operating conditions;

guaranteed operating point efficiencies and poweroutput;

cavitation characteristics;

pressure fluctuations at the draft tube inlet, at thespiral case inlet and on the head cover of themachine;

runaway speed ;index test and flow velocity distribution in various

locations.

In addition, mechanical measurements are oftencarried out, such as torque and bending moment onguide vanes, runner axial thrust etc....

A hill chart corresponding to the model test of atypical Francis hydro-turbine is reported Fig. 2.

Fig. 3 Reduced Scale Model of a Francis Turbineinstalled on the EPFL PF1 Test Rig

2.3. Standard cavitation testsStandard cavitation tests consist in investigating theinfluence of cavitation development on the hydrauliccharacteristics and the type of cavity susceptible todevelop during the operation of the prototype machine.

These investigations are very important for the

evaluation of the setting levels

h of the machine to

the tail-water levela

Z , see Fig. 4, defined as:

s r ah Z Z= (m)

According to the IEC standard nomenclature, the

Net Positive Suction specific Energy, NPSE, of ahydraulic machine is the difference of the specific


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1

Z

Z I

Za

2

hs

Z ref

ZcD

Fig. 4 Setting level definitions for a hydraulic machine

energy at Section 2, with the specific energy due to

the vapor pressurev

p , referred to the reference level

refZ of the machine.

2

2

2 2

2 2

v

ref

v

ref

pNPSE gH gZ

pp C

gZ gZ

=

= + +

(Jkg-1)

For a turbine, it can be assumed that all the specific

kinetic energy at the turbine outlet is dissipated in

the tail race water channel therefore NPSE can be

approximated as follows,

2

2

2

a v

s

p p CNPSE gh

+ (Jkg-1)

Meanwhile for a storage pump or a pump-turbine in

pumping mode, the intake of the machines should

have negligible specific energy losses and therefore

the NPSEcan be approximated as follows

a v

s

p pNPSE gh

(Jkg-1)

Depending on the reference quantities chosen either

the Thomas cavitation factor , so called Thoma

number or the net positive suction specific energy

coefficientc

can be chosen to define a dimension-

less cavitation number.

NPSE

E= ,

2 2

2c

NPSE

R

=

In both cases, we can observe that these terms are

simply related to the setting levels

h , which is easily

determined. However, the problem arises in estimating

the static pressure at the low-pressure section c of

the runner. The mean specific energy conservation

law between these sections leads to the following

expression for the absolute pressure pc,

( )2

2

c v c

ref c rd

p p CNPSE g Z Z E

= + + (Jkg- 1)

whererd

E is the mean specific energy losses between

the sections c and 2 of the draft tube. According to

the flow direction, these losses are positive for a

turbine and negative for a pump.

The corresponding dimensionless expression allows

introducing a local cavitation factorE

related to

as follows

2

2

1

2

ref cc v cE rd

Z Zp p CeE D EFr

= = + +

where the Froude number is defined as

EFr

gD=

The necessary condition of cavity onsetv

p p= in

the runner is then, expressed by the condition:

ECp =

with the pressure factor defined as:

cp p pC

E=

Thus, it is apparent that the static pressure will strongly

depend on the operating point of the machine, even

though the Thoma cavitation number is kept constant.

This can be shown by introducing the discharge

coefficient of the machine.

For a turbine we have:2

2

0

2

11 ref c

E rd

Z Ze

DFr

+ = + +

where 0 corresponds to the discharge operation with

minimum whirl.

Therefore, from the expression of the cavitation

factorE

we see that as much the discharge is

increased, the pressure decreases up to reach the

pressure vapor. For this extreme condition we have:

0E

=

For the case of reference taken at the runner outlet,

by neglecting the draft tube loss factor and assuming

a whirl free condition we have:2

0E

= leading to

21c

.

Therefore, the above ratio allows us to introduce

the dimensionless cavitation number, which expresses

the margin to vapor pressure that we have for a turbine.

We have reported Fig. 5 the values corresponding

to the specific speed of turbines taken from [18]. We

see that in practice, the setting of a turbine requires

that r fulfill the condition:

2

1.8

=


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Fig. 5 cavitation number as a function of specific

speed for the turbines taken from [18]

For a pump with a pure axial inlet flow, we have

in the same way

2

2

1 1ref cE rd

Z Ze

D kFr

= + + ,

where kis a pure geometric factor to take into accountthat the reference section can be arbitrarily selected.

In the case of a reference section taken at the

impeller eye, this factor reduces to unity.

1ck k= =

So, in both types of machines the local value of the

cavitation coefficient is strongly affected by the

discharge coefficient . We can observe that for a

given operating point, cavitation tests are in similitude

with the prototype flow provided the Thoma numbers

and the Froude numbers are the same in both cases,

model scale and prototype scale. Owing to the scalelength factor between the prototype and the model of

large units, it is often impossible to fulfill the Froude

similarity requirement. For example, if we consider

a runner diameter of 5 m operating at 500 Jkg- 1and

the runner diameter of the corresponding model being

0.4 m, the Froude similitude leads to a test specific

energy of 40 Jkg-1, which is far too low for testing.

Thus, very often the test head is higher than the

corresponding Froude head and in turns the cavity

vertical extension on the blades is squeezed by the

scale effects. A way to overcome as much as possiblethe influence of the Froude number is to define a

reference level of the machine as close as possible to

the elevation where cavity development takes place.

Therefore, for vertical axis machines it is strongly

recommended to define the low pressure elevation

levelc

Z as a reference.

Nevertheless, standard cavitation tests are performed

for different operating points by keeping constant the

specific energy coefficient and following the in-

fluence of the Thoma number on the efficiency

and the discharge coefficient . Typical curvesfor a Francis turbine are reported Fig. 6.

Fig. 6 Cavitation curve for a Francis turbine, by keepingconstant the machine specific energy coefficientand for a given guide vane opening angle.

While is decreased, observations of the cavitation

onset and the cavity development are reported.

Characteristic values of are defined such as:

i :onset of visible cavities;

0 : lowest value of sigma for which the efficiencyremains unchanged;

1 : 1% drop of efficiency.

2.4. Type of Cavitation and Setting Level

The objective of cavitation tests being to determine

the setting level of the machine in order to overcome

any efficiency alteration and to minimize the erosion

risk, each type of cavitation is considered with respect

to its dependence on the value of the setting level

and to the erosion risk.

On the one hand, the onset of a leading edge cavity

is more influenced by the blade geometry and the

flow incidence angle than the value of . This meansthat increasing to a very high value of in order toprevent a leading edge cavity development will cause

unacceptable costs. Thus, this type of cavity, which

cannot be avoided for off-design operation, has to be

considered with respect to the erosion risk. In this

case, the Thoma number is determined according to

an acceptable cavity development.

On the other hand, cavity development corresponding

to the design operating point such as bubble cavitation

and hub cavity are very sensitive to the Thoma

number value. However, for each case of hydraulic

machine, different types of cavitation arise dependingeither on the blade design and the operating point or

on the Thoma number value. Thus, it is important to

examine, for each case of hydraulic machine, the type

of cavitation, which occurs in the operating range.

3. CENTRIFUGAL PUMPS

3.1. Type of Cavitation

Cavity development in a centrifugal pump is fully

controlled by the discharge coefficient according to

the relative flow velocity incidence angle at the im-

peller inlet, Fig. 7, which strongly affects the pressuredistribution on the blades at the inlet, [9], Fig. 8.


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W

Cm0

U

CmCm0W

W

Q0Q


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Fig. 13Typical eroded areas of a pump impeller.

A very good correlation is obtained between thecavity development observations made during model

tests and the field observations of the eroded area onthe corresponding prototype impeller, Fig. 14.

Fig. 14 Cavitation erosion of a storage pump impeller

compared to the leading edge cavitation develop-ment as observed during testing of the homologousreduced scale model.

In the case of unshrouded impellers, tip clearancecavities appear and can erode either the pump casingor the blades themselves.

Statistical values of power statistical relation betweenthe acceptable value of the Thoma cavitation numberand the pump specific speed are provided Fig. 15.

4. FRANCIS TURBINES


In the case of a Francis turbine and for the design oper-ating range, the type of cavity developing in the runner

is closely driven by the specific energy coefficient ,

the flow coefficient influencing only the cavity whirl.

High and low values of correspond to a cavity onset

at the leading edge suction side and pressure side of theblades respectively, see Fig. 16. This type of cavitationis not very sensitive to the value of the Thoma numberand it can lead to a severe erosion of the blades.

Traveling bubble cavitation takes place for the designvalue of , at the throat of the runner flow passage,

Fig. 15Statistical acceptable values of Thoma cavitationnumber as a function of pump specific speeds.

Fig. 16Inlet edge cavitation, Francis turbine.

Fig. 17Traveling bubble cavitation in a Francis turbinerunner.

close to the outlet and corresponds to low flowangles of attack. This type of cavitation, see Fig. 17,

is very sensitive to the content of cavitation nucleiand to the value of the Thoma number. For thisreason, the plant NPSE is determined with respect to

this type of cavitation. The drop of the -curve isnoticed when cavities extend up to the runner outletin both types of cavitation.

Depending on the value of the flow coefficient , awhirl cavity develops from the hub of the runner to thecenter axis of the draft tube in the bulk flow, as shownFig. 18. The size of the cavity is dependent of , butthe vortex motion depends only on the flow coeffi-cient values. According to the outlet flow velocity

triangle of Fig. 18, inverse runner rotation of the vortexcorresponds to high flow regime and leads to a large


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axi-symmetric fluctuating cavity. In turn, low flowregimes are responsible for a helical shape of the whirl,rotating at a speed, between 0.25 and 0.4 times therunner rotational frequency. The whirl developmentis mainly concerned with the stability of machineoperation, since it is the main source of pressurefluctuations in the hydraulic installation [20].

Cu U

W

Cm

C

Cu U

Cm

W

C

Fig. 18Cavitation whirl at low and high dischargeoperation, in a Francis turbine discharge ring.

At low flow regime, one can observe complex flowrecirculation at the inlet of the runner leading tovortex cavitation attached to the hub and extendingup to the blade to blade passage, see Fig. 19. Thistype of turbine operation corresponds usually to off-design operation. However this operation cannot beavoided during for instance the reservoir filling up

period of a new hydro-power generation scheme.

Fig. 19Inter blades cavitation vortices in a Francisturbine runner.

Fig. 20 Limits of cavitation development within theoperating range of a Francis turbine:1 - Suction side leading edge cavitation limit;2 - Pressure side leading edge cavitation limit;

3 - Interblade cavitation vortices limit;4 - Discharge ring swirl cavitation limits.

The different limits corresponding to the developmentof each type of cavitation are reported in the hillchart of Fig. 20.

4.2. Effic iency Alteration

The setting of a Francis turbine is determined accord-ing to the risk of efficiency alteration, which is higherfor high discharge, or high load, operating conditionsas it can be seen from the expression of the cavitationfactor

E . Therefore, the runner is usually designed in

such a way that this corresponds to the developmentof traveling bubble outlet cavitation, Fig. 17. Thistype of cavitation is very sensitive to the content ofcavitation nuclei and to the value of the Thomanumber, [17]. For this reason, the plant NPSE isdetermined with respect to this type of cavitation.

Fig. 21Influence of free stream nuclei content onefficiency cavitation curves.

However, many tests carried out at EPFL, [4], [16],for Francis turbine of different specific speeds confirma strong influence of cavitation nuclei content combinedwith the test head on the efficiency alteration phenome-non by cavitation, Fig. 21 and Fig. 23. Nuclei contentdoes not only influence cavitation inception, [19], butalso the development of bubble traveling cavities [3].

Moreover, test head influence is found to be morerelated to an effect of the active nuclei content thanof the Froude effect. According to the RayleighPlesset stability analysis the lower radius limit of anactive nucleus depends directly on the test head valueleading to more or less active nuclei for a givennuclei distribution.

Fig. 22Influence of head and cavitation nuclei contenton Francis turbine cavitation curves


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The cavitation curves reported Fig. 21, are obtainedaccording to the usual cavitation tests. In addition,air micro-bubbles are seeded in the upstream vesselin order to vary the free stream cavitation nucleicontent. It can be observed that, for a given thresholdvalue of the nuclei content, the efficiency is no longeraffected by increasing the nuclei content, the cavitation

coefficient being kept constant.Moreover, the efficiency alteration is strongly relatedto the cavitation extent on the blade as it is confirmed

by flow visualizations. Photographs reported Fig. 23,correspond to the cavitation curves of a test head of20 m in order to overcome any Froude effect on thecavity extent. Photographs A, B are taken for the samelow value of 0.052 and correspond to a low nucleicontent and to a saturated state, respectively. One canobserve that the performance alteration is mainly dueto the vaporization of a part of the blade to blade channelregion which is under the vapor pressure. Thus, the

saturation phenomenon occurs when the active nucleiamount is large enough to occupy all this region.

Fig. 23Flow visualization of traveling bubble cavitationdevelopments corresponding to the A, B & Cpoints of Fig. 23.

Fig. 24 Statistical acceptable values of Thoma cavitationnumber as a function of Francis turbine specific speeds.

Evidence of the strong dependency between the volumeof vapor and efficiency drop can be found in comparing

the photographs B and C, taken for closely the sameefficiency drop of 0.2 %. Even though, the sigma

value of point C, = 0.039, is rather lower than thevalue of case B, the nuclei content in the case C issmall enough to lead to a same volume of vapor andthen to the same performance drop.

The drop of the -curve is noticed when cavities ex-tend up to the runner outlet in both types of cavitation.

Statistical values of power statistical relation betweenthe acceptable value of the Thoma cavitation numberand the specific speed are provided Fig. 24 for aFrancis turbine.

4.3. Cavitation Erosion

Typical runner areas where cavitation erosion can beobserved are reported Fig. 25.

In general severe cavitation erosion damages areobserved in Francis runners on the blade suctionsides, shaded area A of Fig. 25 or downstream in the

blade to blade channel, shaded area B of Fig. 25.

Fig. 25Typical eroded areas of a Francis runner.

Fig. 26Typical erosion at the wall of the blade suction sidedue to inlet edge cavitation, shaded area A of Fig.25.

Fig. 27Typical erosion at the wall of the blade suction sidedue to inlet edge cavitation, shaded area B of Fig. 25.

The cause of those types of erosion, Fig.26 and Fig.

27,

is due to unexpected leading edge cavitation devel-opment Fig. 16 and can only be corrected by reshapingthe inlet edge. However, wall erosion can be mitigated

by welding a layer of cavitation resistant alloy.

In case of development of traveling cavitation bubbleat the runner outlet region, Fig. 17, a "frosted" areacan be observed, shaded area C of Fig. 25., which


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usually leads to barely visible erosion, Fig. 28, andis easily controlled by the Thoma cavitation number.

Fig. 28"Frosted" area at the wall of the runner bladetrailing edge due to outlet traveling bubblecavitation, shaded area C of Fig. 25.

Finally, low load inter-blade cavitation vortices, Fig.19,can lead to erosion of the runner hub wall, shadedarea D of Fig. 25 and Fig. 29.

Fig. 29Typical erosion at the wall of the runner hub dueto inter-blades cavitation vortices, shaded area Dof Fig. 25.

5. KAPLAN AND BULB TURBINES


Runners of Kaplan and bulb turbines are axial withadjustable blade pitch angle and the control of boththe guide vane opening and the blade pitch angleallows optimized operation of the machine, so called"on cam" operation.

For the design operating range a cavity developmenttakes place at the hub of the runner, Fig. 30. Thistype of cavitation is very sensitive to the Thomanumber. Any effect of the water cavitation nucleicontent is observed for this type of cavitation [14].However, the air entertainment can have a greatinfluence on the extent of this cavity, [22].

Since the blades are adjustable, the runner is notshrouded and, then as shown Fig. 31, tip clearancecavitation takes place in the gap between the bladesand the machine casing, leading to an erosion risk eventhough the head could be low. This type of cavitationis driven by the flow shear layer in this gap and it isnot very dependent of the Thoma cavitation number.

Since the blades are adjustable, the runner is not

shrouded and, then as shown Fig. 31, tip clearancecavitation takes place in the gap between the blades

and the machine casing, leading to an erosion risk eventhough the head could be low. This type of cavitationis driven by the flow shear layer in this gap and it isnot very dependent of the Thoma cavitation number.

Fig. 30Hub cavitation development for a Kaplan runner

Fig. 31Tip clearance and hub cavitation for a Kaplanrunner

Even for the case of on cam operation, leading edgecavities can be observed at the inlet of the runner butcan be avoided by improving the shape of the bladeleading edge [12].

The different zones in the hill chart corresponding toeach type of cavitation development are reported

Fig. 32.

0,2

0,6

1,0

1,4

1,8

2,2

2,6

0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

a =cste / A=cste

1

2

/

/

3

=0,90

0,96

0,94

1

0,99

0,98

Fig. 32Limits of cavitation development within the

operating range of a Kaplan turbine;1 - Leading edge suction side cavitation limit,2 - Leading edge pressure side cavitation limit,3 - Hub cavitation limit.

5.2. Effic iency Alteration

The efficiency alteration for a Kaplan and bulbsturbines is mainly due to the development of hubcavitation, Fig. 30.

As this hub cavity reaches the blade trailing edge,we can notice an efficiency drop, Fig. 33. This typeof cavitation has already mentioned is very sensitive

to the Thoma number and determines the plantNPSE of the machine.


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Fig. 33Efficiency cavitation curve for a Kaplan Turbine.

Fig. 34Cavitation development forPlant

Depending on the head of the machine limiteddevelopment of tip clearance cavitation can beadmissible for plant NPSE, Fig. 34.

Fig. 35Influence of Thoma cavitation number on Kaplan

runaway speed.

Fig. 36 Statistical acceptable values of Thoma cavitationnumber as a function of Kaplan turbine specific speeds.

Especially for the case of Kaplan or bulb turbines, itcan be noticed a strong influence of the Thomacavitation number on the runaway speed, Fig. 35.

Statistical values of power statistical relation betweenthe acceptable value of the Thoma cavitation number

and the specific speed are provided Fig. 36 forKaplan turbines.

5.3. Cavitation Erosion

Typical Kaplan runner areas where cavitation erosioncan be observed are reported Fig. 37.

Fig. 37Typical eroded areas of a Kaplan runner.

Fig. 38Typical erosion at the tip of the runner blade andat the discharge ring due to inter-blades cavitationvortices, shaded area D of Fig. 25.

The most critical area where cavitation erosion isobserved are the blade tips and the machine casing,shaded area A and B of Fig. 37. This erosion, Fig. 38,is due to the development of tip clearance cavitation,which can take place even at plant NPSE, Fig. 34.

Fig. 39 Typical erosion at the suction side of the blade dueto leading edge cavitation, shaded area E of Fig. 25.

Either for lasting operations at high head or at lowhead erosion takes place at the suction side or the

pressure side of the runner inlet, dashed area D or Eof Fig. 37 respectively. This type of erosion is caused

by inlet edge cavitation, Fig. 39. Erosion correspondingto dashed area F or G of Fig. 37 can occurs during last-ing low head operation. Finally, for high load operationconditions erosion can be observed at the outlet of therunner at the suction side, shaded area C of Fig. 37.

CONCLUSION

A survey of the different types of caviation featuredby hydraulic machinery has been carried out. Thissurvey finally emphasizes the importance of modeltesting for defining the proper setting level of themachines. The determination of the plant NPSE of amachine is a subtle process, which should include:

the type of cavitation developments the runner orthe impeller is experiencing over the operatingrange of interests;


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the risk of cavitation erosion associated to thistype of cavitation;

the risk of performance alteration.

However, the assessment of those cavitation develop-ments can take benefits in a large extent by developingmonitoring instrumentation for the free stream cavi-

tation nuclei, which can influence the cavitation devel-opment, [8]. Moreover, with respect to the cavitationerosion, relevant indirect method, such as measurementof vibratory levels, can be very useful for quantifyingthe risk during model tests, [5]-[7], [9] and [11].

ACKNOWLEDGMENTS

I would like to acknowledge all my colleagues of theEPFL Laboratory for Hydraulic Machines. I am verygrateful to all the doctorate students I had the

pleasure to supervise in the field of cavitation andhydraulic machinery.

REFERENCES

[1] IEC, "Hydraulic Turbines, Storage Pumps and Pump-Turbines-Model Acceptance Tests". IEC 60193 Standard,International Electrotechnical Commission; Genve,Nov. 1999.

[2] Arn C., Avellan F., Dupont P.; "Prediction of FrancisTurbines Efficiency Alteration by Traveling BubbleCavitation", Proc. 19th IAHR Symp. HydraulicMachinery and Systems, Vol. 1, pp. 534 543,Singapore, 9-11 Sept. 1998.

[3] Avellan, F., Henry, P.; "Theoretical and experimentalstudy of the inlet and outlet cavitation in a model of a

Francis turbine", Proceedings of 12th I.A.R.H. Sym-posium on Hydraulic Machinery in the Energy RelatedIndustries, paper 1-3, pp 38-55, Stirling, August 1984.

[4] Avellan, F., Gindroz, B., Henry, P., Bachmann, P.,Vullioud, G., Wegner, M.; "Influence de la chute d'essaiet de la nuclation sur les performances en cavitationdes modles de turbines Francis", Proceedings of13th I.A.H.R. Symposium on Progress in Technology,vol. 1, pp 2.1-2.15, Montral, September 1986.

[5] Avellan, F., Dupont, Ph.,Farhat, M.; "Cavitation ErosionPower", Proceedings of the First ASME-JSDME FluidsEngineering Conference, FED-Vol. 116, pp. 135-140,Portland, Oregon, USA, 23-27 June 1991.

[6] Bourdon, P., Simoneau, R., Lavigne, P., "A vibratoryapproach to the detection of erosive cavitation", Proc.of International Symposium on Cavitation Noise andErosion in Fluid Systems, ASME Winter AnnualMeeting, San Francisco (USA), FED: Vol. 88, Dec1989, pp 95-102.

[7] Bourdon P., Farhat M., Simoneau R., Pereira F., DupontPh., Avellan F., Dorey J.-M.; "Cavitation ErosionPrediction on Francis Turbines Part 1: Measurementson the Prototype", Proceedings of the 18th IAHRSymposium on Hydraulic Machinery and Cavitation,Valencia, Spain, Vol. 1, pp. 534-543, September 1996.

[8] Brand, C., Avellan, F.; "The IMHEF system forcavitation nuclei injection", 16th Symposium of the

IAHR section on Hydraulic Machinery and Cavitation,So Paolo (Brazil), 14-18 September 1992.

[9] Dorey J.-M., Laperrousaz E., Avellan F., Dupont Ph.,Simoneau R., Bourdon P.; "Cavitation ErosionPrediction on Francis Turbines Part 3: Methodologiesof Prediction", Proceedings of the 18th IAHRSymposium on Hydraulic Machinery and Cavitation,Valencia, Spain, Vol. 1, pp. 564-573, September 1996.

[10]Dupont P., Parkinson E., Avellan F., Walther W.; "Cavita-tion development in a centrifugal pump: numerical and

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[11]Dupont Ph., Caron J.-F., Avellan F., Bourdon P.,Lavigne P., Farhat M., Simoneau R., Dorey J.-M.,Archer A., Laperrousaz E., Couston M.; "CavitationErosion Prediction on Francis Turbines Part 2: ModelTests and Flow Analysis", Proceedings of the 18th IAHRSymposium on Hydraulic Machinery and Cavitation,Valencia, Spain, Vol. 1, 574-583, September 1996.

[12]Favre, J. N., Avellan, F., Ryhming, I. L., "Cavitationperformance improvement by using a 2-D inverse methodof hydraulic runner design", Proceedings of Interna-

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[13]Gindroz, B., Avellan, F., Henry, P.; "Similarity rulesof cavitation tests: the case of the FRANCIS turbine",Proceedings of 14th I.A.H.R. Symposium on HydraulicMachinery: Progress within Large and High SpecificEnergy, pp. 755, 766, Trondheim (Norway), June 1988.

[14]Gindroz, B., Avellan, F., "Rgles de similitude dans lesessais de cavitation", Comptes rendus des XXe Journesde l'Hydraulique de la Socit Hydrotechnique deFrance, Papier I.18, pp. 1-8, Lyon (France), avril 1989.

[15]Gindroz, B., Avellan, F., Henry, P.; "Guide lines forperforming cavitation tests", Proceedings of IAHR15th Symposium on Modern Technology in HydraulicEnergy Production, Vol. I, paper H1, 11 pages,Belgrade, Yugoslavia, 11-14 September 1990.

[16]Gindroz, B., Henry, P., Avellan, F.; "Francis cavitationtests with nuclei injection", 16th Symposium of theIAHR section on Hydraulic Machinery and Cavitation,So Paolo (Brazil), 14-18 September 1992.

[17]Henry, P, "Influence of the amount of bubble nucleion cavitation tests of a Francis turbine", Proc. of theASME Symposium, Cavitation and Polyphase FlowForum,pp. 23-28, Fort Collins,12-14 June 1978.

[18]Henry, P.; "Turbomachines hydrauliques. Choix illustrde ralisations marquantes", Presses polytechniques

et universitaires romandes, 412 pages, Lausanne, 1992.[19]Holl, J.W., Wislicenus, G. F.; "Scale effects on

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[20]Jacob, T., Prenat, J. E.; "Generation of hydro-acousticdisturbances by a Francis turbine model and dynamicbehavior analysis", Proceedings of IAHR 15th Sympo-sium on Modern Technology in Hydraulic EnergyProduction, Vol. 2, paper T4, Belgrade, Yugoslavia,11-14 September 1990.

[21]Strohmer, F., Nichtawitz, A., "Influence of the dissolvedair content and head on cavitation test of bulb turbine",Proceedings of 14th I.A.H.R. Symposium on HydraulicMachinery: Progress within Large and High SpecificEnergy, pp. 779, 786, Trondheim (Norway), June 1988.

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